Electromagnetic instability in a periodic alternating gradient quadropole focusing system

Summary form only given. A stability analysis has been formulated for an arbitrary periodic alternating gradient quadrupole system by applying the Floquet theory. For simplicity, the dispersion relation for a sinusoidal alternating gradient quadrupole system was also obtained. A sinusoidal alternating gradient quadrupole system may be represented as a superposition of right-hand, and left-hand helical quadrupole fields. An orbit-unstable regime (in the absence of electromagnetic waveguide modes) and various electromagnetically unstable regimes (three-wave instabilities) were found. Analytic decomposition of the beam modes of the dispersion relation provided analytic expression for the boundaries of the various unstable regimes in parameter space. Stability regimes for the alternating gradient quadrupole system have been compared to those associated with a helical quadrupole